It has been hitherto known that 4- (hydroxymethylphosphinyl)-oxobutanoic acid is an useful production intermediate of L-AMPB having herbicidal activity (see patent documents 1, 2 and 3; and non-patent document 1).
Also, it is only known as a method for synthesizing 4-(hydroxymethylphosphinyl)-oxobutanoic acid that 3-(alkoxymethylphosphinyl)-propionic acid ester (-propionate) or 3-(hydroxymethylphosphinyl)-propionic acid ester and oxalic acid diester are subjected to condensation reaction, then subjected to hydrolysis and decarboxylation (see patent document 4). In addition, it is known as a method for synthesizing 3-(hydroxymethylphosphinyl)-propionic acid ester that methylphosphinic acid is subjected to an addition reaction with acrylic acid ester (acrylate) (see patent document 5 and non-patent document 2). On the other hand, 3-(alkoxymethylphosphinyl)-propionic acid ester is synthesized such that methyldichlorophosphine is subjected to an addition reaction with acrylic acid, then the produced acid chloride is subjected to a reaction with alcohol (see non-patent documents 3 and 4).    Patent document 1: JP Kokai Publication H01-27485A    Patent document 2: JP Kohyo Publication 2003-528572A    Patent document 3: JP Kokai Publication S59-184196A    Patent document 4: JP Kokai Publication S56-92897A    Patent document 5: JP Kokai Publication H05-247068A    Non-Patent document 1: J. Org. Chem., 56, 1783-1788 (1991)    Non-Patent document 2: Angw. Chem. Int. Ed. Engl., 20, 223 (1981)    Non-Patent document 3: Zh. Obshch. Khim., 42, 1730(1972)    Non-Patent document 4: Zh. Obshch. Khim., 37, 710 (1967)